Present values of CDO tranches.

ccording to the general recipe (
Risk neutral
pricing
), the time
value of the coupon payments of the tranche
is given
by
where the
are the coupon payment dates and
.
The
is the coupon rate. It is
tranche-dependent:
As always in these notes, the
denotes the time
value of riskless zero coupon bond with maturity
.
The time
value of the protection/loss leg of the tranche contract is
Note that we do not change to the T-forward measure as we did in
(
Credit_default_swap_section
).
Instead, we assume that the defaults and interest rates are independent.